The equation of a circle is given below. $(x+1.6)^{2}+(y+9.8)^{2} = 26$ What is its center? $($
Explanation: Standard equation of the circle A circle is the collection of all points at a distance ${r}$ from a center $({h},{k})$. We can use the Pythagorean theorem to write an equation to relate the center and radius. $({h},{k})$ ${r}$ $x-{h}$ $y-{k}$ $(x, y)$ $\begin{aligned} a^2+b^2&=c^2\\\\ (x - {h})^2 + (y - {k})^2 &= {r}^2 \end{aligned}$ Rewriting the given equation We can rewrite the given equation as: $\begin{aligned}(x+1.6)^{2}+(y+9.8)^{2} &= 26\\\\ (x - {(-1.6)})^2 + (y - {(-9.8)})^2 &= { 26}\end{aligned}$ Finding the center According to the rewritten equation, we can see that the center of the circle is $({-1.6}, {-9.8})$. Finding the radius According to the standard equation of the circle, we get that ${r^2}={26}$. Rounding the radius to two decimal places, we get that $r={\sqrt{ 26}} \approx {5.10}$. Summary The circle is centered at $(-1.6, -9.8)$. The circle has an approximate radius of $5.10$ units.